But my logic is missing something: who could receive the resumés and "hire" the best ones? wouldn't that get easily corrupted, especially since it's a single failure point?
It most certainly would.
I was of the opinion that democracy is the least worst regime, or the best we have for now, as you say, but I recently figured out that it might not be. There's a case to be made that
maybe monarchy mixed with constitution would be better. My rationale is that, if there's a king, then he'll most certainly steal from the people, just as in ancient civilizations. However, king's royal family will remain in power for decades, if not for hundreds of years. This means that, his stealing will be moderated. For example, he won't completely rip off all the citizens, because the future and prosperity of his people will directly influence the future of his family. On the other hand, when a politician knows that he might not be elected in four years, he'll steal as much as possible for as long as he's in power.
This is an important difference in time preference of the nation. In a modern democracy, politicians often make decisions which impact the lives of not-even-yet born people, like by borrowing money. They are incentivized to be more reckless with the future generation. In contrast, a king is likely to consider the long-term consequences more carefully, as his family's future and the throne itself could be at risk.
Just food for thought.
It's more complicated than that.
A king would steal for his family and for his extended family, and, depending on the king, not on how long the dynasty was ruling, will matter in how much he will steal (some are greedier than others).
On the same way some politicians steal more, some steal less.
Some kings were smart and thoughtful and helped society advance, some not (royal blood doesn't necessarily means one is inclined to learn and meant to rule).
Same goes for politicians: some try to even do good, some others are there only for stealing.
Some politicians get to stay longer, some are changed faster.
Some kings and dynasties lasted longer, some not. Keep in mind that kings got killed a lot only for succession. Keep in mind that royal families can end up with no children or only girls, shifting the dynasty into a different family's hands.
And keep in mind that modern royalty is only a façade and in many cases it's a democratic government actually governing, getting us back to our "beloved" democracy.
This being said, imho you are only partly right and a king is not necessarily better than a democracy, especially as a king doesn't accept other institution say "nope, you cannot do that, tough luck" (and this earns one point to the democracy).